KULeuven Energy Institute

TME Branch

WP EN2014-28

Short-term demand response of flexible electric heating systems: an integrated model

Dieter Patteeuw, Kenneth Bruninx, Lieve Helsen & William D‘haeseleer

TME WORKING PAPER - Energy and Environment Last update: March 2015

An electronic version of the paper may be downloaded from the TME website:

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Short-term demand response of flexible electric heating systems: an

integrated model.

Dieter Patteeuw, Kenneth Bruninx, Erik Delarue, Lieve Helsen and William D’haeseleer

August 14, 2014

Abstract

Active Demand Response (ADR) can contribute to a more (cost-)efficient operation of and investmentin the electric power system as it provides the needed flexibility to cope with the intermittent character ofrenewables. One of the promising demand side technologies in terms of ADR are electric heating systemsas they allow to modify their electric load pattern without affecting the thermal energy service they deliver,due to the thermal inertia in the system. However, these systems are hard to describe with traditionaldemand side models, since the performance depends on boundary conditions (occupants behaviour, weatherconditions) and the thermal losses in the system are non-linear. This paper presents an integrated systemmodel, taking into account the dynamics and constraints of both electricity supply and heating systems. Onlysuch an integrated system approach is able to simultaneously consider all technical and comfort constraintspresent in the system.

1 Introduction

Demand side management (DSM) is a (market) concept that actively uses options at demand and supply sideto modify electricity demand to increase customer satisfaction and coincidentally produce desired changes inthe electric utility’s load shape [1]. If applied correctly, DSM could come with a variety of benefits, such as a re-duced electricity generation margin, higher operational efficiencies in production, transmission and distribution,more effective investments, lower price volatility, lower electricity costs and the possibility to manage highlyintermittent renewables (see, amongst others, Strbac [2], Callaway et al. [3], Kirschen [4] and Newsham [5]).In this paper, the focus is on short-term load shifting, one of the aspects of DSM, which will be referred to asActive Demand Response (ADR) [1].

ADR can be facilitated by dispatchable load programs (direct load control, curtailable load, demand bid-ding) and/or price-based programmes (real-time pricing, time-of-use pricing, peak pricing), each with its ownopportunities and drawbacks. However, residential consumers are generally not willing to forfeit the foreseenend-use of the electric energy as the benefits they perceive (e.g. a lower electricity bill) do not outweigh thedrawbacks [3]. For example, most consumers would require very high incentives to turn off their lights, as thisenergy service is considered to be very valuable. Some demand side technologies though contain some formof (virtual) electrical energy storage, which can be used to affect the electric load pattern perceived by theelectric power system without tampering with the quality of the energy services provided. Typical (residential)examples of these technologies [3] are

• Thermostatically controlled loads, such as boilers, heat pumps, refrigerators and air conditioners;

• Plug-in electric vehicles;

• Deferrable loads, such as washing machines and dish washers.

Similarly, industrial consumers could shift some of their production, if some product could be (intermediately)stored. The storage allows these customers to simultaneously be fully responsive and non-disruptive in termsof the perceived energy service [3].

However, many challenges remain to be overcome before a large scale roll-out of flexible demand side tech-nologies will emerge. One of these challenges is the quantification of the benefits – for consumer and producers– of ADR programs [2]. Many studies include or even focus on ADR. However, often the supply side or thedemand side is represented too simplistically. When the focus is on the supply side of the electric power system,the demand is represented via a price elastic demand or via virtual generator models [6]1. Looking at the

1The virtual generator models (VGM) are denoted as ‘dispatchable load models’ by De Jonghe. In this paper, VGM is used tostress the similarity between the constraints on the demand side technology and those employed to describe a generator.

1

demand side, a price profile is typically used to represent the supply side [7–9]. All of these modeling techniqueshave proven their merits, but are inadequate to study the true interaction between supply and demand side,especially when storage type customers are involved as shown in [10,11].

In this paper, a modeling framework based on a system approach is introduced that has been used tostudy ADR in [10, 11]. A physical model of the demand side technology will be integrated in a traditionalunit commitment model (see Section 2). The electric heating systems considered in this paper and in [10, 11]consist of heat pumps and auxiliary electric resistance heaters that provide both domestic hot water (DHW) andspace heating (SH) via radiators. This system is designed to guarantee a certain thermal comfort level (e.g. acertain range on indoor temperatures and hot water when desired) and is characterized by large thermal inertia.Thermal energy storage is provided via the hot water storage tank and the thermal mass of the residence. Asthese small scale systems can be installed in large numbers and control access to these loads could be veryinexpensive with the advent of communication platforms, they are good candidates for ADR [3].

This working paper presents the integrated model and the data used for the case study presented in thepaper ‘Integrated modeling of active demand response with electric heating systems’ [11]. First, a generaldescription of the integrated model is presented in Section 2, after which the models for supply side (Section3) and demand side (Section 4) are described. Finally, the data used for and assumptions adopted in the casestudy are presented in Section 5.

2 Integrated model

The integrated model describes an optimization problem, in which the overall operational cost of providing thedemanded electric power (Eq.(1)) is minimized, subject to technical and comfort constraints of both the supplyside (Eq. (2)– (18)) and the demand side (Eq. (19)–(35). This mixed integer linear programming (MILP)model combines a unit commitment (UC) and economic dispatch (ED) model on the supply side with a detailedrepresentation of the physical – thermal and electric – behavior of the considered demand side technology.The model is implemented in GAMS 23.7 and MATLAB R© 2011b, using the MATLAB R©–GAMS coupling asdescribed by Ferris [12]. CPLEX 12.5 is used as solver.

Via the UC and ED model, the commitment status (binary decision variable z) and hourly output of eachpower plant(real decision variables g) are determined so that the electricity demand is met at the lowest overalloperational cost, taking into account the technical constraints of the power plants. These constraints includethe minimum and maximum output, the ramping rates and minimum on and off times of each power plant.The operational cost consists of fuel, emission and start-up costs. The formulation of the model employed inthis paper is inspired by [13] and is described in detail in Section 3. In the integrated model, the demandfor electricity that needs to be met consists of two parts: a fixed electricity demand profile and the electricitydemand from the flexible demand side technology. The latter electricity demand is an optimization variable,determined through the demand side model.

This demand side model describes – in this case study – the physical behavior of the electric heating systems,which deliver heat for domestic hot water production and space heating. The thermal behavior of the residenceand domestic hot water storage tank is modeled through a linear state space model (states T and inputs U ,real decision variables). This model allows to convert a certain demand for thermal comfort in a demand forelectric power for each dwelling. Summing and scaling these demand profiles allows to simulate a certain marketpenetration of flexible heating systems. Thermal energy storage in the residence envelope and the hot waterstorage tank allows to shift the electric power demand of these electric heating systems in time. The constraintson the thermal comfort required by the occupants – e.g. temperature constraints and the availability of hotwater – results in constraints on the electric power demand and on the flexibility offered to the supply side.This demand side model is described in detail in Section 4.

In this integrated model, it has been assumed that demand and supply are controlled centrally. Thisabolishes the need to set up a real-time pricing system. However, if the price signal used in such a real-timepricing system would correctly reflect the cost of electricity and reactions of the demand side to this price signalwould be correctly reflected in changes in that price profile, the demand and supply side would interact asobtained from the integrated model [10].

3 Supply side model

The power plants are dispatched in such a way that the operational cost of generating the demanded electricalpower over the simulated time period is minimized. This cost c(g, z) consists of fuel costs (FCi,j), start-up costs(SCi,j), ramping costs (RCi,j) and CO2-emission costs (CO2Ti,j). The objective function reads

min c(g, z) =∑i

∑j

FCi,j + SCi,j +RCi,j + CO2Ti,j (1)

2

where I is the set of power plants present in the model (index i) and J is the set of time steps (index j, onetime step is one hour). The fuel cost (FCi,j) is determined by the fuel price and the efficiency of the powerplant:

∀i,∀j : FCi,j ≥ Ci · zi,j +MAi ·(gi,j − PMINi · zi,j

)(2)

where Ci is the fuel cost for running the plant at its minimum power level and zi,j is the commitment status ofplant i.MAi is the marginal cost for the additional generation level above its minimum power level (gi,j−PMINi ·zi,j). This is a linear approximation of the quadratic cost curve of a power plant. The CO2 cost CO2Ti,j,s isbased on the emissions, the load level and a fixed CO2 price per ton CO2P :

∀i,∀j,∀s : CO2Ti,j,s ≥ CO2P ·[Bi · zi,j +MBi ·

(gi,j,s − PMINi · zi,j

) ](3)

Similar as the fuel costs, the CO2 cost consists of a fixed part (the emissions when a plant is running on itsminimum power level Bi) and a term accounting for the marginal emissions of different generation levels (MBi).The start-up cost SCi,j is calculated as

∀i,∀j : SCi,j = StCoi · vi,j (4)(5)

with a fixed start-up cost, different per power plant and fuel, StCoi. The binary variable vi,j is equal to 1 attime step j if the plant starts up at that time step j. In this model, we have not differentiated between hot andcold start-ups. Finally, the ramping costs RCi,j are determined via the following equations:

∀i,∀j : RCi,j ≥ RCPi ·(gi,j − gi,j−1 − PMINi · vi,j

)(6)

∀i,∀j : RCi,j ≥ RCPi ·(gi,j − gi,j−1 − PMINi · wi,j+1

)(7)

with binary variable wi,j indicating a shut-down of power plant i on time step j and RCPi a cycling cost forpower plant i.

The demand and supply side models are coupled by the market clearing condition, meaning that supplyand demand for electricity must be equal at all time steps j. The demand for electricity consists of the fixedelectricity demand dfixj and the variable electricity demand d

varj . The latter is the total electricity demand

resulting from flexible electric heating systems. This is an optimisation variable in itself and is determined viathe demand side model (Section 4) and a factor mp that represents the market penetration. In the equationbelow, gi,j is the generation level of power plant i at time step j.

∀j : dfixj +mp · dvarj =∑i

gi,j + curj · gRESj (8)

∀j : 0 ≤ curj ≤ 1 (9)

with gRESj the infeed from renewable energy sources at timestep j. Decision variable curj stands for the relativecurtailment of renewable energy and has a value that varies between 0 (full curtailment) and 1 (no curtailment).

This optimization is subject to a number of constraints. In this model, the transmission and distributiongrid was not taken into account for the sake of simplicity. The power plants have several technical constraints,different per fuel and technology. The operational range of power of a power plant is limited to a minimum(PMINi ) and maximum (P

MAXi ) output level. The following constraints must hold for the gi,j , the total

generation of power plant i on time step j:

∀i,∀j : gi,j ≤ PMAXi · zi,j (10)∀i,∀j : gi,j ≥ PMINi · zi,j (11)∀i,∀j : gi,j ≥ 0 (12)

(13)

where the binary variable zi,j indicates the on-off status of power plant i at time step j. The ramp-up andramp-down rates of the power plants have been included as follows:

∀i,∀j : gi,j ≤ gi,j−1 + ∆PMAX,+i · (1− vi,j) + PMINi · vi,j (14)

∀i,∀j : gi,j ≥ gi,j−1 −∆PMAX,−i · (1− wi,j)− PMINi · wi,j (15)

The ∆PMAX,+i (maximum ramping-up[MWhour

]) and ∆PMAX,−i (maximum ramping-down

[MWhour

]) values are

derived from the maximum ramping rates of the power plants. The binaries vi,j and wi,j indicate a start-up,

3

respectively a shut down of a power plant i (see below). Note that at start-up or shut-down, we force eachpower plant to run at its minimum output level for one hour. The minimum up- and down-times have beenincluded in the model as in Rajan and Takriti [14]. If the power plant i is started up in time j, then it mustremain on for the next MUT − 1 time periods (and similarly when shut down). For every time step j that apower plant i starts up, respectively shuts down, the following constraints must hold:

∀i,∀j :MUT−1∑

k=1

vi,j−k ≤ zi,j (16)

∀i,∀j :MDT−1∑

k=1

wi,j−k ≤ 1− zi,j (17)

where the binary variable wi,j equals 1 if the plant i is shut down at time step j and J is the number of timesteps considered in the optimization. The on-off status zi,j of each power plant is linked to the start-up andshut-down variables as follows:

∀i,∀j : zi,j − zi,j−1 + vi,j − wi,j = 0 (18)

For a detailed discussion on this unit commitment model, the reader is referred to [13].

4 Demand side model

The demand side model presented below allows the determination of the electricity demand of the flexible electricheating systems 2. A verification of this demand side model with respect to a detailed physical simulation modelusing the IDEAS package [15] in Modelica, can be found in [16].

The variable electricity demand dvarj is the total electricity demand resulting from flexible electric heatingsystems. The electricity demand of a set of S (index s) representative residences is summed and scaled up withthe factor mp (Eq. (8)) to represent this variable demand in case of a significant market penetration of flexibleelectric heating systems. As the electricity demand of each residence is the sum of the electricity demand of theheat pump (PHPs,j ) and the auxiliary heater (P

AUXs,j ), the total variable electricity demand becomes (see Fig. 1)

∀j : dvarj =∑

s

P elj,s =∑

s

PHPs,j + PAUXs,j (19)

with P els,j the electricity demand of the electric heating systems in residence s during time step j. The thermaldemand that these systems need to satisfy in each residence s on each time step j stems from comfort constraints,enforced via a model for space heating (Section 4.1) and DHW production (Section 4.2). Each residence is

assumed to have an air coupled heat pump (HP) that can deliver both domestic hot water Q̇HP,DHWs,j and space

heating Q̇HP,SHs,j (see Fig. 1). The heat pump is equipped with a back-up electric resistance heater (AUX),

which can be used for space heating Q̇AUX,SHs,j and for domestic hot water production Q̇AUX,DHWs,j . The system

is schematically represented in Fig. 1. The electricity demand of the heating systems in each residence can berelated to the thermal power supplied to that residence as follows:

∀s, j : P els,j =Q̇HP,SHs,j

COPHP,SHs+Q̇AUX,SHs,jηerh

+Q̇HP,DHWs,j

COPHP,DHWs+Q̇AUX,DHWs,j

ηerh(20)

with ηerh the efficiency of the electric resistance heaters. Heat pumps are efficient electric heating systems,using electricity to extract and convert low temperature heat to heat at temperatures suitable for space heatingand/or hot water production. Air coupled heat pumps extract heat from the ambient air Q̇EXTs,j (See Fig. 1).

Their coefficient of performance or COPHP is a measure of the amount of heat a heat pump delivers per unitof electricity and depends on the temperature at which the heat pump absorbs heat (the ambient air T e) andthe temperature at which the heat pump delivers heat (the supply water to the radiators T sup):

COPHP = ηex ·T sup

T sup − T e(21)

with ηex the exergetic efficiency of the heat pump [9]. Since the supply water temperature is a state of the

system directly affected by the decision variable Q̇HP,SHs,j , the inclusion of equality constraint (21) in the demandside model would result in a non-linear optimization problem, as denoted by Verhelst et al. [9]. Verhelst et al.suggest to use a constant value for the COPHPs , based on the expected value of the supply water temperature

2Cooling is not considered in this model, since one considers residential buildings in a Belgian climate which do not need coolingif built according to good practice.

4

PHPs,j Q̇EXTs,j P

AUXs,j

heat pump (HP)COP

Q̇HP,SHs,j Q̇AUX,SHs,j

auxiliaryheater (AUX)

ηerh

Q̇AUX,DHWs,jQ̇HP,DHWs,j

Q̇INTs,jQ̇SOLs,j

hot water tankstate space model

building modelstate space model: T SHs,j

Q̇DEM,DHWs,j Q̇LOSS,DHWs,jQ̇

LOSS,SHs,j

Figure 1: The demand for hot water (DHW) and space heating (SH) in each dwelling s on each timestep j – corrected for the internal Q̇INTs,j and solar gains Q̇

SOLs,j – must be satisfied by thermal power

(Q̇AUX,DHWs,j ,Q̇AUX,shs,j ,Q̇

HP,DHWs,j ,Q̇

HP,SHs,j ) supplied by the auxiliary heater (AUX) and the heat pump (HP). The

combined electricity consumption of these electric heating systems (PAUXs,j ,PHPs,j ), summed over all dwellings and

multiplied by the market penetration of the flexible heating systems, makes up the total variable electricitydemand. The residences and the hot water tanks are modeled via a state space model (see Section 4.2 & 4.1).The heating systems (heat pumps & electric resistance heaters) are modeled via their efficiencies (ηerh, COP ).

of the radiators Tsup,exp and the average ambient air temperature Te. This approach can be applied when the

power profile is smooth. From the ambient air temperature and the expected supply water temperature, theCOPHPs can be determined prior to the optimization as

∀s : COPHPs = COP0 + c1 · Te

j + c2 · Tsup,exp (22)

in which COP0, c1 and c2 are constants fitted to catalog data. The thermal power supplied by each of theelectric heating systems is limited by the maximal electric power each system can consume:

∀s, j :Q̇HP,SHs,j

COPHP,SHs+

Q̇HP,DHWs,j

COPHP,DHWs≤ PHPmax (23)

∀s, j :Q̇AUX,SHs,jηerh

+Q̇AUX,DHWs,j

ηerh≤ PAUXmax (24)

∀s, j : Q̇HP,SHs,j , Q̇HP,DHWs,j , Q̇

AUX,SHs,j , Q̇

AUX,DHWs,j ≥ 0 (25)

in which PHPmax and PAUXmax represent the maximal electric power that can be consumed by the heat pump and

the auxiliary heater. Note that the heat pump and the auxiliary heater can deliver both space heating anddomestic hot water during the same hour, in which these systems supply heat at full power to the space heatingfirst, after which heat is supplied to the domestic hot water tank during the rest of that hour.

4.1 Building model

The building model consists of one zone, heated via radiators. The thermal behavior of the building equippedwith radiators is described by a state space model (Eq. (26)).

∀s, j : T SHs,j+1 = A · T SHs,j +B · USHs,j (26)

This model allows to relate the states (i.e. temperatures in the system) T SHs,j and inputs (i.e. thermal power

supplied to the system & the temperature of its surroundings) USHs,j through state space matrices A and B.These matrices make up a linear model that describes the thermal conductances and capacities in the system,along with linear approximations of the convective and radiative heat transfer coefficients. The state space

5

matrices are based on [17]. The building model as an equivalent circuit of thermal conductances and capacitiesis shown in Fig 2. The state vector T SHs,j holds all modeled temperatures in the residence which are decisionvariables in the optimization problem:

T SHs,j = [Tairs,j T

fs,j T

wis,j T

roofs,j T

wes,j ]. (27)

The five states in the model are the temperatures of the indoor air T airs,j , floor Tfs,j, internal wall T

wis,j , roof

T roofs,j and external wall Twes,j . The input vector U

SHs,j holds all thermal powers supplied to the system and the

temperatures of the surrounding air T ej and ground Tground:

USHs,j = [Q̇HP,SHs,j Q̇

AUX,SHs,j T

ej T

ground Q̇SOLj Q̇INTj ]. (28)

The inputs T ej , Tground, Q̇SOLj and Q̇

INTj are disturbances to the system, and hence uncontrollable. Q̇

SOLj is the

heat gain due to solar radiation and Q̇INTj the internal heat gain due to occupants and appliances. The thermal

powers supplied by the heat pump Q̇HP,SHs,j and the auxiliary heater Q̇AUX,SHs,j are the controllable inputs and

hence decision variables.As thermal comfort must be achieved, the temperatures in the heated zones are constrained to temperatures

that are perceived as comfortable. If the occupants are present in residence s, the temperature in the heatedzone T zs,j should neither exceed T

max, nor fall below Tminp (occupants present and awake) or Tminnp (occupants

absent or sleeping):

∀s, j : Tminp · occs,j + Tminnp · (1− occs,j) ≤ T airs,j ≤ Tmax (29)

In this equation occs,j is a binary parameter which is 1 when the occupants are present and awake in residences at time step j and 0 when they are not.

4.2 Domestic hot water tank model

The hot water storage tank is assumed to be a perfectly stirred water tank, i.e. all the water in the tank is atthe same temperature T tanks,j at time step j. The water in the hot water storage tank can either be heated up by

the heat pump, Q̇HP,DHWs,j or by the back up electric heater Q̇AUX,DHWs,j . The demand for hot water is converted

to a heat demand Q̇dems,j (Eq. (32)). The discretized version of the law of conservation of energy for the storagetank reads

∀s, j : ρ · Vtank · cpT tanks,j+1 − T tanks,j

∆t= Q̇HP,DHWs,j + Q̇

AUX,DHWs,j − Q̇

DEM,DHWs,j −G · (T

tanks,j − T sur) (30)

with ρ and cp the density and heat capacity of water. Vtank is the volume of water in the tank. In Eq.(30) it isassumed that Vtank is constant: hot water taken from the tank is instantaneously replaced by an equal amountof cold water. With ∆t the time step of the optimization, the time derivative of T tanks,j can be approximated asT tanks,j+1−T

tanks,j

∆t . The term G · (Ttanks,j −T sur) determines the heat loss Q̇

LOSS,DHWs,j to the surroundings at a constant

temperature T sur. The thermal conductance between the hot water and the surroundings G[WK

]is assumed

equal to that of the insulation around the hot water storage tank.The temperature of the cold tap water T cold and the temperature of the demanded hot water T dem are both

assumed to be constant. A three way valve is used to mix water from the hot water tank at T tanks,j to the desired

temperature T dem. Applying conservation of energy and mass for the three way valve, one can determine therequired volumetric flow rate from the tank V̇ tanks,j as a function of the demanded flow rate V̇

dems,j at temperature

T dem:

∀s, j : V̇ tanks,j = V̇ dems,j ·(T dem − T cold)(T tanks,j − T cold)

(31)

The demand for hot water, i.e. the thermal power that needs to be delivered by the hot water tank, can berelated to the temperature of the demanded water and the volumetric flow rate by applying conservation ofenergy on the hot water storage tank. Substituting Eq. (31) in the resulting expression yields

∀s, j : Q̇dems,j = ρ · cp · (T tanks,j − T cold) · V̇ tanks,j = ρ · cp · (T dem − T cold) · V̇ dems,j (32)

Note that Q̇dems,j is independent of the temperature of the water in the tank. This relation holds if and only if

T tank is higher than T dem.

6

The lower boundary for water tank temperature stems from the requested water temperature. When theoccupants desire hot water, the tank must be heated up to at least T dem. Otherwise, the tank water temperaturecan get as low as T cold:

∀s, j : T tanks,j ≥ T dem · hwds,j + Tcold · (1− hdws,j) (33)

with hwds,j a binary parameter which is 1 when hot water is demanded in residence s on time step j and 0when this is not the case.

The heat pump can deliver heat to the hot water tank up to a maximum temperature THP,max, typically60 ◦C, which is lower than the maximum allowed temperature of the tank T tank,max, typically 90 ◦C. Only theauxiliary electric heater AUX can supply heat at temperatures above THP,max. These constraints are enforcedvia the binary variable xs,j:

∀s, j : T tanks,j +∆t

ρ · Vtank · cp· Q̇HP,DHWs,j ≤ (1− xs,j) · T

HP,max + xs,j · T tank,max (34)

∀s, j :Q̇HP,DHWs,j

COPHP,DHWs≤ (1− xs,j) · PHP,max (35)

If xs,j is zero, the tank water temperature is lower than THPmax (Eq. (34)) and output of the heat pump is limited

by its maximal electric capacity (Eq. (35)). If the tank water temperature T tanks,j exceeds THPmax, xs,j is one (Eq.

(34)) and the output of the heat pump is set to zero (Eq. (35)). In that case, Eq. (34) sets an upper boundaryon the temperature of the tank water.

5 Case study: data & assumptions

This section describes the data used in the case study in the paper ‘Integrated modeling of active demandresponse with electric heating systems’ [10,11]. Firstly, the assumed generation system and its techno-economicalparameters are discussed. Secondly, the assumptions on the demand side are presented.

5.1 Supply side

Demand for electricity is met through renewable energy sources (RES) and conventional generation. Electricityin-feed from RES is treated as a demand correction and can be curtailed if this yields a lower system cost3. Theconventional generation capacity is used to balance the residual electric load. The technical characteristics ofthe power plants inspired on those of the Belgian power system and are summarized in Table 1. In the partialloading characteristics, the power levels are given as percentages of the nominal power while the efficiency isgiven in absolute values. Ramp-up and ramp-down constraints are assumed equal. The start-up costs dependon the fuel. The relative efficiency A allows to calculate the efficiency η of the power plant in partial loading(output g) conditions via the following equation:

η(g) = η(PMAX) ·[1 +A · ln

( gPMAX

)](36)

For the nuclear power plants, pressurized water reactors (PWR), it has been assumed that the efficiency is notaffected by the partial loading of the power plant.

The supply side of the electric power system considered consists of 1 nuclear power plant (1200 MW), 5coal-fired steam power plants (4000 MW), 10 gas-fired combined cycle power plants (4000 MW) and 10 peakingunits (1000 MW). The prices of the various fuels and their carbon content have been taken from [18,19]. Thesevalues are shown in Table 1 below. Throughout the simulations, a CO2-price of 30

EURton CO2

has been assumed.The fixed demand profile used is based on hourly demand data for Belgium for 2010 [20]. The week with

the total energy consumption closest to the yearly average is selected. The profile is preserved and scaled toequal 90% of the peak power of the supply system. If variable demand is present, the resulting demand profileis re-scaled to represent a certain percentage of the total electric energy demand. RES infeed data are providedby the Belgian TSO [20]. The week with the total RES energy in-feed closest to the weekly average value for2010 has been selected. The profile is preserved and rescaled to satisfy a certain percentage of the total energydemand of that week. To limit calculation times, only the first 48 hours of both profiles are retained.

3Curtailment costs are assumed to be internal transfers within the model. The only net cost perceived by the system is theopportunity cost of not using the zero-cost RES power available.

7

Table 1: Technical characteristics of the power plants in the model. Sources: [20–23], own calculations.

Technology Fuel Efficiency Dynamics

Un

itsi

ze[M

W]

Fu

el

Fu

elco

st[

EU

RO

MW

hprim

]

CO

2-c

onte

nt

[tC

O2

MW

hprim

]

Pm

in[%P

MA

X]

Rel

ati

veeffi

cien

cyA

[−]

Ram

p-u

p[ %PM

AX

min

]M

in.

up

-tim

e[h

]

Min

.d

own-t

ime

[h]

Ram

pin

gco

st[E

UR

MW

]

Sta

rt-u

pco

st[E

UR

]

PWR UO2 1200 2 0 50 0 1 8 8 0 21,000SPP Coal 800 12 0.338 43 0.08 1 6 3 1.8 27,520

CCGT Gas 400 25 0.205 35 0.20 6 2 1 1 6,300GT Gas 100 25 0.205 30 0.30 10 1 1 0.8 1,272ICE Oil 100 35 0.281 35 0.30 10 1 1 0.8 1,484

5.2 Demand side

In order to represent a population structure, 25 representative households are considered. In this case study,the number of households of each household size is inspired by the population structure of Belgium [24] and isgiven in Table 2. All residences (Section 5.2.2) are of the same type, in other words A and B in Eq. (26) areidentical. Each household has a different user behavior: the occupants are present at different times of the day.Therefore, comfort constraints (Section 5.2.1) are enforced on different time steps for each residence s. Theoccupancy depends on the number of inhabitants and is based on the model of Richardson et al. [25]. The hotwater tank is sized to hold exactly the amount of hot water that is used in a day, which can effect the sizing ofthe heating systems (Section 5.2.3).

5.2.1 Comfort constraints

According to Peeters et al. [26], the temperature of the heated zone must be above 20 ◦C in living rooms (Tminp )

and above 16 ◦C in bedrooms (Tminp ) when occupants are present. This temperature should not exceed 24◦C

in both living rooms and bedrooms (Tmax).The demand for hot water is based on Peuser et al. [27]. The hot water demand differs according to the

number of inhabitants. The first and second inhabitant are expected to use 50 liter per person per day, thefollowing inhabitants use 30 liter per person per day [28]. The demanded water temperature is assumed to be60 ◦C. The specific moments that inhabitants use DHW is randomly divided over the moments the inhabitantsare present, while the cumulative demand mimics the hot water demand profile of a large apartment block aslisted by Peuser et al [27].

5.2.2 Building

The considered building represents a typical Belgian detached residence built after 2005, as determined in theTABULA project [29]. From these parameters, Reynders et al. [17] constructed a detailed physical simulationmodel by applying the IDEAS package [15] in Modelica. From this detailed physical simulation model, Reynderset al. [17] determine multiple reduced order models in the form of thermal RC-networks, from which the fivestate model (figure 2) performed the best. The parameters of this thermal RC-network are translated to thematrices A and B in Eq. (26).

The weather data (Belgium, 2008) is obtained from Meteonorm [30]. The solar heat gains Q̇sol are determinedvia the model developed by Baetens et al. [15]. The weather conditions used in this paper are for a mild Belgianwinter week (Fig. 3).

The internal heat gains are dependent on the presence of the occupants in the residence. When the occupantsare present, appliances produce 250 W , while each resident represents a 50 W heat gain. When the occupantsare absent, internal gains are set to zero.

5.2.3 Heating systems

The considered building is equipped with radiators with a nominal supply water temperature of 45 ◦C anda nominal return water temperature of 35 ◦C. The electric heating systems are modeled via their efficiency,

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Figure 2: Thermal RC-network representation of the reduced order building model [17]. The five states in themodel are the temperatures of the indoor air (air), floor (f), internal wall (wi), roof (roof) and external wall(we). The temperature of the external air (e) and ground (ground) are inputs to the system.

Table 2: The number of households per household size, inspired by the population structure in Belgium [24].

Household size [persons] 1 2 3 4 5 6Households [-] 8 8 4 3 1 1

e.g. Eq. (21). The efficiency of the electric resistance heaters is 100%. The efficiency of the heat pumps isapproximated via Eq. (22). The parameters COP0, c1 and c2 were determined by Verhelst et al. [31] as a linearfit of heat pump data from a heat pump manufacturer and are respectively 5.593, 0.0569 and −0.0661 . Theexpected supply water temperature for the radiator T sup,exp is 45 ◦C, leading to a COPHP,SHs of 3.08 in caseof temperatures as shown in Fig. 3. If the heat pump supplies hot water to the hot water storage tank, thisexpected supply temperature is 60 ◦C, leading to a COPHP,DHWs of 2.60.

The heating system is sized based on the maximal heat demand Q̇DOT at the design operation temperatures(DOT). This maximal heat demand is taken to occur at an ambient temperature of −10 ◦C, a ground temper-ature of 10 ◦C and an indoor temperature of 20 ◦C. The different heating systems are sized according to Eq.(37) to (38). The heat pump is typically sized at 80% of this maximal power in order operate more in intervalswith better part load efficiency. According to [32], the heat pump still supplies about 97% of the space heatingthroughout the year in this case. The heat pump is thus sized at 4065 kWe. The hot water storage tank is sizedto hold exactly the amount of hot water that is used in one day. The heating of this hot water storage tankis typically sized to heat up the tank in 2 hours, leading to a maximum thermal power demand of Q̇DHW,max.For the sake of redundancy, the auxiliary heater is sized to meet the maximum of the peak demand for spaceheating or domestic hot water demand, see Eq. (38).

PHP,max =0.80 · Q̇DOTCOPDOT

(37)

PAUX,max = max(Q̇DOT , Q̇DHW,max) (38)

6 Conclusion

Active Demand Response (ADR) could lead to a variety of benefits, such as a reduced electricity generationmargin, higher operational efficiencies in electricity production, transmission and distribution, more effectiveinvestments, lower price volatility, lower electricity costs and the possibility to manage highly intermittentrenewables. Correct quantification of these benefits is one of the main challenges that need to be overcomebefore a large scale roll-out of flexible demand side technologies can take place.

To this end, an integrated modeling approach was presented which can be used to study the interactionbetween supply of and demand for electricity. The demand side technology considered in this paper is that offlexible electric heating systems. The modeling approach is compared against other, simplified models employedto study ADR in the paper called ‘Short-term demand response of flexible electric heating systems: the needfor integrated simulations’ [10]. A more extensive comparison between this integrated modeling approach andother modeling techniques, is discussed in the paper called ‘Integrated modeling of active demand response withelectric heating systems” [11].

9

5 10 15 20 25 30 35 40 450

5

10

15

Time [h]

Ambienttemperatu

re[◦C]

0

1,000

2,000

3,000

Solarhea

tgains[W

]

Figure 3: Ambient temperature (solid line) and solar gains (dashed line) for a mild Belgian winter week. Theweather data (Belgium, 2008) is obtained from Meteonorm [30].

The presented model may be used by other researchers that investigate the effect of ADR on the electricpower system. Especially if one is interested in the effect of the market penetration of an ADR technology, thepresented model could be useful. In addition, demand aggregators may use this work to develop operationalmodels to schedule and optimize their use of thermostatically controlled loads in ADR programs.

Beyond this work, further expansion of the model, as well as validating the presented model on larger datasets could further strengthen this research. Second, the aggregation of different residential consumers – whichwas out of the scope of the presented paper – merits further research.

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http://www.gams.com/dd/docs/tools/gdxmrw.pdfhttp://www.gams.com/dd/docs/tools/gdxmrw.pdfhttp://www.mech.kuleuven.be/en/tme/research/energy_environment/Pdf/wpen2013-11.pdfhttp://www.mech.kuleuven.be/en/tme/research/energy_environment/Pdf/wpen2012-15http://www.mech.kuleuven.be/en/tme/research/energy_environment/Pdf/wpen2012-15http://www.elia.be/en/grid-datahttps://www.entsoe.eu/resources/data-portal/http://www.mech.kuleuven.be/en/tme/research/energy_environment/Pdf/wpen2013-05.pdfhttp://www.mech.kuleuven.be/en/tme/research/energy_environment/Pdf/wpen2013-05.pdfhttp://statbel.fgov.be/nl/statistieken/cijfers/bevolking/structuur/huishoudens/http://statbel.fgov.be/nl/statistieken/cijfers/bevolking/structuur/huishoudens/

Patteeuw_IntegratedSimulations_ThermalSystems_ModelDescription_12082014.pdfIntroductionIntegrated modelSupply side modelDemand side modelBuilding modelDomestic hot water tank model

Case study: data & assumptionsSupply sideDemand sideComfort constraintsBuildingHeating systems

Conclusion